Prove that : `tan^(-1) x+cot^(-1) y = tan^(-1) ((xy+1)/(y-x))`

Prove that : tan^(-1) x + cot^(-1) (1+x) = tan^(-1) (1+x+x^2)

Prove that tan^(-1) x + cot^(-1) (x+1) = tan ^(-1) (x^(2) + x+1) .

Prove that tan^(-1)(x+1)+tan^(-1)(x-1)=tan^(-1)((2x)/(2-x^2))

Prove that : 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) = tan^(-1) x

Prove that : tan^(-1)((x-y)/(1+xy)) + tan^(-1)((y-z)/(1+yz)) + tan^(-1)( (z-x)/(1+zx)) = tan^(-1)((x^2-y^2)/(1+x^2y^2))+tan^(-1)((y^2-z^2)/(1+y^2z^2))+tan^(-1)((z^2-x^2)/(1+z^2x^2))

Prove that : sin cot^(-1) tan cos^(-1) x=x

Prove that tan(cot^(-1)x)=cot(tan^(-1)x)

Prove that tan(cot^(-1)x)=cot(tan^(-1)x)

tan^(-1)x-tan^(-1)y=tan^(-1)((x-y)/(1+xy)) holds good for

The result tan^(-1)x-tan^(-1)y = tan^(-1)((x-y)/(1+xy)) is true when the value of xy is "………."